how to write a good (maths) ph.d. thesis - university of...
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How to write a good (maths) Ph.D. thesis
Melina A Freitag
Department of Mathematical SciencesUniversity of Bath
Postgraduate Away Day3rd February 2012
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The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
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Outline
The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
3 of 30
University requirements
A Ph.D. shall be awarded to a candidate who shall have
1. pursued a programme of study as prescribed under Regulation 16.5(b)
2. presented a thesis on the candidate’s advanced study and research whichsatisfies the Board of Examiners as:◦ making an original and significant contribution to knowledge◦ giving evidence of originality of mind and critical judgement in a particular
subject◦ containing material worthy of peer-reviewed publication◦ being satisfactory in its literary and/or technical presentation and structure
with a full bibliography and references◦ demonstrating an understanding of the context of the research: this must
include, as appropriate for the subject of the thesis, the scientific,engineering, commercial and social contexts
3. and passed a viva voce examination conducted by the examiners on thebroader aspects of the field of research in addition to the subject of thethesis...
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Outline
The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
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University regulations for submitting a Ph.D. thesis
• For details seehttp://www.bath.ac.uk/student-records/pgresources/
• Number of copies and submission procedure:◦ about two months before submission - HD1 form.◦ 3 soft bound copies to Graduate Office - HD2 form.◦ hard bound copies and electronic submission to library only after the viva.
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University regulations for submitting a Ph.D. thesis
• For details seehttp://www.bath.ac.uk/student-records/pgresources/
• Number of copies and submission procedure:◦ about two months before submission - HD1 form.◦ 3 soft bound copies to Graduate Office - HD2 form.◦ hard bound copies and electronic submission to library only after the viva.
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University regulations for submitting a Ph.D. thesis
• Paper and layout - double or single sided.
• Typeface and spacing - 11pt or 12pt, easy readable font.
• Numbering of pages.
• Title page and copyright declaration.
• Table of contents and abstract/summary.
• Follow the University regulations for margin sizes/linespacing/fonts/binding etc.
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University regulations for submitting a Ph.D. thesis
• Paper and layout - double or single sided.
• Typeface and spacing - 11pt or 12pt, easy readable font.
• Numbering of pages.
• Title page and copyright declaration.
• Table of contents and abstract/summary.
• Follow the University regulations for margin sizes/linespacing/fonts/binding etc.
7 of 30
University regulations for submitting a Ph.D. thesis
• Paper and layout - double or single sided.
• Typeface and spacing - 11pt or 12pt, easy readable font.
• Numbering of pages.
• Title page and copyright declaration.
• Table of contents and abstract/summary.
• Follow the University regulations for margin sizes/linespacing/fonts/binding etc.
7 of 30
University regulations for submitting a Ph.D. thesis
• Paper and layout - double or single sided.
• Typeface and spacing - 11pt or 12pt, easy readable font.
• Numbering of pages.
• Title page and copyright declaration.
• Table of contents and abstract/summary.
• Follow the University regulations for margin sizes/linespacing/fonts/binding etc.
7 of 30
University regulations for submitting a Ph.D. thesis
• Paper and layout - double or single sided.
• Typeface and spacing - 11pt or 12pt, easy readable font.
• Numbering of pages.
• Title page and copyright declaration.
• Table of contents and abstract/summary.
• Follow the University regulations for margin sizes/linespacing/fonts/binding etc.
7 of 30
University regulations for submitting a Ph.D. thesis
• Paper and layout - double or single sided.
• Typeface and spacing - 11pt or 12pt, easy readable font.
• Numbering of pages.
• Title page and copyright declaration.
• Table of contents and abstract/summary.
• Follow the University regulations for margin sizes/linespacing/fonts/binding etc.
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Presentation and style
• Typical:
1. Title page (listing author, title, department, type of degree, year andmonth of submission).
2. Declaration that work has not been used in another degree.3. A copyright statement.4. A list of notation.5. A brief statement of author’s research career.6. Acknowledgements and dedications.7. Table of contents.8. List of Figures.9. List of Tables.
10. Abstract/Summary.
11. THE ACTUAL WORK
• Opening pages: indication which parts have been published.
• Optional: index.
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Presentation and style
• Typical:
1. Title page (listing author, title, department, type of degree, year andmonth of submission).
2. Declaration that work has not been used in another degree.3. A copyright statement.4. A list of notation.5. A brief statement of author’s research career.6. Acknowledgements and dedications.7. Table of contents.8. List of Figures.9. List of Tables.
10. Abstract/Summary.11. THE ACTUAL WORK
• Opening pages: indication which parts have been published.
• Optional: index.
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Presentation and style
• Typical:
1. Title page (listing author, title, department, type of degree, year andmonth of submission).
2. Declaration that work has not been used in another degree.3. A copyright statement.4. A list of notation.5. A brief statement of author’s research career.6. Acknowledgements and dedications.7. Table of contents.8. List of Figures.9. List of Tables.
10. Abstract/Summary.11. THE ACTUAL WORK
• Opening pages: indication which parts have been published.
• Optional: index.
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Outline
The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
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Content
• Self-contained.
• May include more than one topic.
• Include more details than a paper.
• It is like a book.
• No unnecessary material. Most theses are too long.
• Organisation and structure is important.
• Who are you writing for? (your supervisor(s), internal and externalexaminer)
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Content
• Self-contained.
• May include more than one topic.
• Include more details than a paper.
• It is like a book.
• No unnecessary material. Most theses are too long.
• Organisation and structure is important.
• Who are you writing for? (your supervisor(s), internal and externalexaminer)
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Content
• Self-contained.
• May include more than one topic.
• Include more details than a paper.
• It is like a book.
• No unnecessary material. Most theses are too long.
• Organisation and structure is important.
• Who are you writing for? (your supervisor(s), internal and externalexaminer)
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Content
• Self-contained.
• May include more than one topic.
• Include more details than a paper.
• It is like a book.
• No unnecessary material. Most theses are too long.
• Organisation and structure is important.
• Who are you writing for? (your supervisor(s), internal and externalexaminer)
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Content
• Self-contained.
• May include more than one topic.
• Include more details than a paper.
• It is like a book.
• No unnecessary material. Most theses are too long.
• Organisation and structure is important.
• Who are you writing for? (your supervisor(s), internal and externalexaminer)
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Content
• Self-contained.
• May include more than one topic.
• Include more details than a paper.
• It is like a book.
• No unnecessary material. Most theses are too long.
• Organisation and structure is important.
• Who are you writing for? (your supervisor(s), internal and externalexaminer)
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Content
• Self-contained.
• May include more than one topic.
• Include more details than a paper.
• It is like a book.
• No unnecessary material. Most theses are too long.
• Organisation and structure is important.
• Who are you writing for? (your supervisor(s), internal and externalexaminer)
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Plagiarism - DONT!
• If you copy text put it in quotation marks and cite the source.
• Do not copy proofs of theorems unless it is really necessary for the thesis.
• Your examiners will be particularly alert to plagiarism.
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Grammar, Spelling, Punctuation - DO!
• Use spell checkers!
• Ask a friend/fellow student or family member to read through parts ofyour thesis.
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Structure
Clear communication of original ideas is most important!
Do not waffle!
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Structure
Clear communication of original ideas is most important!
Do not waffle!
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Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
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Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
14 of 30
Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
14 of 30
Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
14 of 30
Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
14 of 30
Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
14 of 30
Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
14 of 30
Structure
• Tell a story (Explain to someone (a mathematician) in 2-3 minutes whatyour thesis is about).
• Give talks to practice your communication skills! Great speakers areusually great writers, too!
• Make an outline early on.
• First chapter(s): describe the problem clearly; put it into context.
• Demonstrate a sound knowledge of existing work, give a critical survey(Literature review).
• What is new/original in your thesis? This should be the main part ofyour thesis (3-4 Chapters).
• For computational projects, normally a comparison with other methods isrequired.
• Conclusions: What have you done? Identify future researchdirections/open problems.
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Structure (more detailed)
• Introduction Define what your research is about; justify why it isimportant; explain your thesis structure.
• Background/Literature Review Put your research into context; giveliterature.
• Methods Explain methods; theoretical approaches.
• Analysis/Results This will include your results. Experiments.Comparison to other methods. Proofs of theorems.
• Interpretation/Discussion Justify your interpretations. Put them intocontext.
• Conclusions Short conclusion. Future research.
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Structure (more detailed)
• Introduction Define what your research is about; justify why it isimportant; explain your thesis structure.
• Background/Literature Review Put your research into context; giveliterature.
• Methods Explain methods; theoretical approaches.
• Analysis/Results This will include your results. Experiments.Comparison to other methods. Proofs of theorems.
• Interpretation/Discussion Justify your interpretations. Put them intocontext.
• Conclusions Short conclusion. Future research.
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Structure (more detailed)
• Introduction Define what your research is about; justify why it isimportant; explain your thesis structure.
• Background/Literature Review Put your research into context; giveliterature.
• Methods Explain methods; theoretical approaches.
• Analysis/Results This will include your results. Experiments.Comparison to other methods. Proofs of theorems.
• Interpretation/Discussion Justify your interpretations. Put them intocontext.
• Conclusions Short conclusion. Future research.
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Structure (more detailed)
• Introduction Define what your research is about; justify why it isimportant; explain your thesis structure.
• Background/Literature Review Put your research into context; giveliterature.
• Methods Explain methods; theoretical approaches.
• Analysis/Results This will include your results. Experiments.Comparison to other methods. Proofs of theorems.
• Interpretation/Discussion Justify your interpretations. Put them intocontext.
• Conclusions Short conclusion. Future research.
15 of 30
Structure (more detailed)
• Introduction Define what your research is about; justify why it isimportant; explain your thesis structure.
• Background/Literature Review Put your research into context; giveliterature.
• Methods Explain methods; theoretical approaches.
• Analysis/Results This will include your results. Experiments.Comparison to other methods. Proofs of theorems.
• Interpretation/Discussion Justify your interpretations. Put them intocontext.
• Conclusions Short conclusion. Future research.
15 of 30
Outline
The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
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Presentation and style
Make your thesis clear and enjoyable to read!You do not want the reader to get angry or bored or both.
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Writing Process - The iterative process
• Start as early as possible.
• You can begin to draft the first chapters in your early months, when youstart to become familiar with the problem - writing also helps tounderstand!
• Publish papers during your time as a graduate student - so you just haveto edit them and put them together.
• Use early reports (6 month/12 month) - of course they will probably berewritten, but it is better to start with something rather than an emptypage.
• Write background and survey material at an early stage - it keeps youenthusiastic!
• A sooner rather than later writing also helps you to become familiar withLATEX.
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Writing Process - The iterative process
• Start as early as possible.
• You can begin to draft the first chapters in your early months, when youstart to become familiar with the problem - writing also helps tounderstand!
• Publish papers during your time as a graduate student - so you just haveto edit them and put them together.
• Use early reports (6 month/12 month) - of course they will probably berewritten, but it is better to start with something rather than an emptypage.
• Write background and survey material at an early stage - it keeps youenthusiastic!
• A sooner rather than later writing also helps you to become familiar withLATEX.
18 of 30
Writing Process - The iterative process
• Start as early as possible.
• You can begin to draft the first chapters in your early months, when youstart to become familiar with the problem - writing also helps tounderstand!
• Publish papers during your time as a graduate student - so you just haveto edit them and put them together.
• Use early reports (6 month/12 month) - of course they will probably berewritten, but it is better to start with something rather than an emptypage.
• Write background and survey material at an early stage - it keeps youenthusiastic!
• A sooner rather than later writing also helps you to become familiar withLATEX.
18 of 30
Writing Process - The iterative process
• Start as early as possible.
• You can begin to draft the first chapters in your early months, when youstart to become familiar with the problem - writing also helps tounderstand!
• Publish papers during your time as a graduate student - so you just haveto edit them and put them together.
• Use early reports (6 month/12 month) - of course they will probably berewritten, but it is better to start with something rather than an emptypage.
• Write background and survey material at an early stage - it keeps youenthusiastic!
• A sooner rather than later writing also helps you to become familiar withLATEX.
18 of 30
Writing Process - The iterative process
• Start as early as possible.
• You can begin to draft the first chapters in your early months, when youstart to become familiar with the problem - writing also helps tounderstand!
• Publish papers during your time as a graduate student - so you just haveto edit them and put them together.
• Use early reports (6 month/12 month) - of course they will probably berewritten, but it is better to start with something rather than an emptypage.
• Write background and survey material at an early stage - it keeps youenthusiastic!
• A sooner rather than later writing also helps you to become familiar withLATEX.
18 of 30
Writing Process - The iterative process
• Start as early as possible.
• You can begin to draft the first chapters in your early months, when youstart to become familiar with the problem - writing also helps tounderstand!
• Publish papers during your time as a graduate student - so you just haveto edit them and put them together.
• Use early reports (6 month/12 month) - of course they will probably berewritten, but it is better to start with something rather than an emptypage.
• Write background and survey material at an early stage - it keeps youenthusiastic!
• A sooner rather than later writing also helps you to become familiar withLATEX.
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Writing Process
• If you have not written up as you go along - plan at least 6 months forwriting up.
• Make a timetable.
• What have you done? What do you still need to do?
• Fill in the gaps.
• Thoroughly read and check before submission - have as many people readit as possible.
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Writing Process
• If you have not written up as you go along - plan at least 6 months forwriting up.
• Make a timetable.
• What have you done? What do you still need to do?
• Fill in the gaps.
• Thoroughly read and check before submission - have as many people readit as possible.
19 of 30
Writing Process
• If you have not written up as you go along - plan at least 6 months forwriting up.
• Make a timetable.
• What have you done? What do you still need to do?
• Fill in the gaps.
• Thoroughly read and check before submission - have as many people readit as possible.
19 of 30
Writing Process
• If you have not written up as you go along - plan at least 6 months forwriting up.
• Make a timetable.
• What have you done? What do you still need to do?
• Fill in the gaps.
• Thoroughly read and check before submission - have as many people readit as possible.
19 of 30
Writing Process
• If you have not written up as you go along - plan at least 6 months forwriting up.
• Make a timetable.
• What have you done? What do you still need to do?
• Fill in the gaps.
• Thoroughly read and check before submission - have as many people readit as possible.
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Writing Process
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Hints and tips for writing
• Try to analyse the work of writers/researchers you like.
• Read a lot of books, maths books, maths theses, maths papers.
• Keep a notebook of ideas.
• Be constructively critical (but positive) of your own work.
• Set yourself short term targets.
• Keep what you have written for a couple of weeks and then re-read it.
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Hints and tips for writing
• Try to analyse the work of writers/researchers you like.
• Read a lot of books, maths books, maths theses, maths papers.
• Keep a notebook of ideas.
• Be constructively critical (but positive) of your own work.
• Set yourself short term targets.
• Keep what you have written for a couple of weeks and then re-read it.
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Hints and tips for writing
• Try to analyse the work of writers/researchers you like.
• Read a lot of books, maths books, maths theses, maths papers.
• Keep a notebook of ideas.
• Be constructively critical (but positive) of your own work.
• Set yourself short term targets.
• Keep what you have written for a couple of weeks and then re-read it.
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Hints and tips for writing
• Try to analyse the work of writers/researchers you like.
• Read a lot of books, maths books, maths theses, maths papers.
• Keep a notebook of ideas.
• Be constructively critical (but positive) of your own work.
• Set yourself short term targets.
• Keep what you have written for a couple of weeks and then re-read it.
21 of 30
Hints and tips for writing
• Try to analyse the work of writers/researchers you like.
• Read a lot of books, maths books, maths theses, maths papers.
• Keep a notebook of ideas.
• Be constructively critical (but positive) of your own work.
• Set yourself short term targets.
• Keep what you have written for a couple of weeks and then re-read it.
21 of 30
Hints and tips for writing
• Try to analyse the work of writers/researchers you like.
• Read a lot of books, maths books, maths theses, maths papers.
• Keep a notebook of ideas.
• Be constructively critical (but positive) of your own work.
• Set yourself short term targets.
• Keep what you have written for a couple of weeks and then re-read it.
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Outline
The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
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Packages
• LATEX and text editors
• baththesis.sty
• MakeIndex
• BibTEX
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Packages
• LATEX and text editors
• baththesis.sty
• MakeIndex
• BibTEX
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Packages
• LATEX and text editors
• baththesis.sty
• MakeIndex
• BibTEX
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Packages
• LATEX and text editors
• baththesis.sty
• MakeIndex
• BibTEX
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Templates
• A useful template for writing a thesis which follows the University ofBath regulations:
http://people.bath.ac.uk/mamamf/baththesis/
• Feel free to download the template and change it to use it for your ownthesis. It follows all the necessary University of Bath requirements.
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BibTEX
• collect your references for your bibliography at an early stage of yourstudies - it will be difficult to hunt them down later.
• BibTEX - a wonderful LATEXprogram for collecting references in .bib fileswhich then can be used in LATEX.
• MathSciNet, Google Scholar, CiteSeer, Mendeley and others.
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BibTEX
• collect your references for your bibliography at an early stage of yourstudies - it will be difficult to hunt them down later.
• BibTEX - a wonderful LATEXprogram for collecting references in .bib fileswhich then can be used in LATEX.
• MathSciNet, Google Scholar, CiteSeer, Mendeley and others.
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BibTEX
• collect your references for your bibliography at an early stage of yourstudies - it will be difficult to hunt them down later.
• BibTEX - a wonderful LATEXprogram for collecting references in .bib fileswhich then can be used in LATEX.
• MathSciNet, Google Scholar, CiteSeer, Mendeley and others.
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Outline
The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
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The Viva
• In the UK: normally you are asked questions.
• Possibly: short talk.
• Read your thesis.
• Opportunity to tell interested people about your research.
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Outline
The purpose of a thesis
University regulations (the easy bit)
Content and structure (the harder bit)
Presentation and writing process
Make your life easier - some helpful LATEX
The defense
Summary
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Summary/Homework
• Your thesis should tell a story (try it!).
• Think about some good maths papers/books you have read, what werethey doing well?
• Start as early as possible.
• Use baththesis.sty early on.
• Have a general structure (chapter titles/outline) in place early on.
• Make a timetable (set short term targets).
• (Re)-read your thesis as often as you can.
• Be positive.
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Know your work cycle!
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N. J. Higham, Handbook of writing for the mathematical sciences,Society for Industrial Mathematics, 1998.
D. Knuth, T. Larrabee, and P. Roberts, Mathematical writing,no. 1193, Mathematical Assn of Amer, 1989.
S. Krantz, A primer of mathematical writing: Being a disquisition onhaving your ideas recorded, typeset, published, read and appreciated,Amer Mathematical Society, 1997.
Questions?
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